an introduction to the jcsda community radiative transfer...

An Introduction to the JCSDA Community RadiativeTransfer Model (CRTM)

Yong HanNOAA/NESDIS

JCSDA

Outline

• The role of a fast radiative transfer model in satellite data assimilation

• CRTM main modules

• Radiative transfer (RT) equation applied

• CRTM surface emissivity/reflectivity models

• RT solution in clear sky environment

• CRTM fast transmittance model

• RT solution in cloudy/aerosol environment

• CRTM Forward, Tangent-linear, Adjoint and K-Matrix models

• CRTM user interface

Why need a fast RT model?

])([)(])([21)()(

21)( 11

mFmT

mbT

b yxyEEyxyxxBxxxJ −+−+−−= −−

• Background model state xb and its covariance B• Measurement ym and its error covariance Em

• Radiative transfer (RT) model y(x) and its error EF

Variational Analysis: the cost function

0)}({)()( 11 =−−−=∂∂ −− xyyExHxxBxJ

mT

b

Minimization:

}{⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

∂∂

==j

iji x

yhxH ,)( Jacobian matrix with respect to state variables

x

• An RT model maps state variables to radiances and it can be used to retrieve information about the state variables from the radiance measurements.

• CRTM is a fast RT model, which employs many computational efficient algorithms to meet the requirements of the operational data assimilation system.

Community Contributions

• Community Research: Radiative transfer scienceUWisc – Successive Order of IterationUniversity of Colorado –DOTLRT UCLA – Delta 4 stream vector radiative transfer modelPrinceton Univ – snow emissivity model improvement NESDIS – Advanced doubling and adding scheme, surface emissivity models, LUT for aerosols, clouds, precipAER – Optimal Spectral Sampling (OSS) MethodUMBC – SARTA

• Core team (ORA/EMC): Smooth transition from research to operationMaintenance of CRTMCRTM interface Benchmark tests for model selection

Integration of new science into CRTM

What CRTM does?

• Compute satellite radiances (Forward model)

• Compute radiance responses to the perturbations of the state variables (Tangent-linear model)

• Compute Adjoint (Adjoint model)

• Compute Jacobians (K-matrix model)

CRTM Major Modules

Forward model

SfcOptics(Surface EmissivityReflectivity Models)

AerosolScatter(Aerosol Absorption

Scattering Model)

AtmAbsorption(Gaseous Absorption

Model)

CloudScatter(Cloud Absorption Scattering Model)

RTSolution(RT Solver) Source Functions

public interfaces

CRTM Initialization

CRTM Destruction

K-matrix model

Tangent-linear model

Adjointmodel

Supported Instruments (IR & MW)

TIROS-N to NOAA-18 AVHRRTIROS-N to NOAA-18 HIRSGOES-8 to 13 Imager channelsGOES-8 to 13 sounder channel 08-13GOES-R ABI Terra/Aqua MODIS Channel 1-10 METEOSAT-SG1 SEVIRI

Aqua AIRSAqua AMSR-E Aqua AMSU-AAqua HSBNOAA-15 to 18 AMSU-ANOAA-15 to 17 AMSU-BNOAA-18 MHS TIROS-N to NOAA-14 MSU

DMSP F13,15 SSM/T1DMSP F14,15 SSM/T2DMSP F16 SSMIS NPP ATMSCoriolis WindsatMETOP-A AMSUA, MHS, HIRS, AVHRR

Specific intensity:

νIthe flux of energy in a given direction per second per unit frequency range per unit solid angle per unit area perpendicular to the given direction

mW/(m2.sr.cm-1)

Brightness Temperature:

νBT

)(1ννν IBBT −=

Kelvin

which is the Inverse of the Planck function

Radiance:

)1(2)( /2

3

−= kThec

hTB ννν

Two of the fundamental variables in CRTM

Atmospheric transmittance:

p

TOA

{)( pντ∫

=−

p

dpp

ep 0

')'(

)(σ

ντe.g. if Is is a upward radiance emitted from the surface, then Isτν(ps) is the amount of energy contribution from the surface received by a satellite sensor. ps

aerosol

Absorbing gases

Surface

Cloud

p(0)p(1)

p(n)p(n-1)

Layer 1

Layer n

Solar radiation &Cosmic background

• The current operational CRTM does not model the Stokes vector; instead CRTM solves the following equation for a scalar intensity:

TVUQI },,,{• Stokes vector:where I = Iv + Ih, Q=…

describes the intensity, phase and polarization of the radiation field.

))(()1()4/)(,,(

')',()',,(4

),(),(

/ τωπτω

ττπωτ

ττμ

μτ TBeFP

dIPId

dI

−+ΩΩ+

ΩΩΩΩ+Ω−=Ω

⊕−⊕⊕

∫

• The current operational CRTM assumes:

(1) the atmospheric radiation is unpolarized (exception: O2 Zeeman absorption and emission in the mesosphere)

(2) Polarization is neglected for IR sensors.

Radiative Transfer Equation

τ --- optical path

CRTM surface emissivity/reflectivity models

θ θPi Pr=(1-ε)Pi

Air

Pi

θ

Air

Bidirectional reflectance distribution function (BRDF):

),()cos(),(),(),,,(

iiiiiii

rrrrrii dI

dIBRDFϕθθϕθ

ϕθϕθϕθΩ

≡iθ

rθ

iϕrϕ

Z

),( rrrdI

x

y

ϕθ),( iiiI ϕθ

idΩrdΩ

Lambertian (perfect rough) surface:πρϕθϕθ =),,,( rriiBRDF

Specular surface:))sin()/(cos()()()(),,,( rriririrriiBRDF θθϕϕδθθδθρϕθϕθ −−=

)(1)( θεθρ −=

Specular surface Rough surface

rrrriiii dBRDF∫ Ω= )cos(),,,(),( θϕθϕθϕθρ

CRTM assumes a specular reflection for MW sensors and Lambertian reflection for IR sensors, and uses relationship: (but is not limited to the

two special cases))(

Reflectance:

θε

Emissivity (by Kirchhoff’s law):),(1),( iiii ϕθρϕθε −=

Polarization in surface emission and scattering (MW)• Emission and scattering by a surface is usually polarization-dependent.• A radiometer with a linearly polarized antenna would measure the same amount of atmospheric

emission (randomly polarized) regardless of the direction of the antenna polarization vector pa; but would receive a different amount of radiation from the surface when the pa vector changes orientation

Scan

Vertically pol.E vector

Vertically pol.E vector

z

Antenna

kk

O O

Surface)(sin)(cos.)( 22 φεφεε hVp polVnadir

a+=

and for h polarization (pa is perpendicular to the scanning plane: )(cos)(sin.)( 22 φεφεε hVp polhnadir

a+= The circles represent the horizontal

polariztion perpendicular to the (k,z) plane)

• Since the atmospheric radiation is assumed unpolarized, we may still use a scalar RT equation to compute a radiance with a polarization pa by using a surface emissivity/reflectivity that is a combination of polarization components.

φ

Over ocean surface

Example: the AMSU sensor has channels with linear polarized antennas. For v polarized antennas (when viewing nadir direction, pa is in the scanning plane):

O

Reflector

Model calculations:solid line for wind speed = 13.5 m/s; dashed line

for 3.5 m/s.Measured:

crosses for wind speed = 13.5 m/s; circles for 0.5 m/s

Pa varies its orientation

CRTM surface emissivity/reflectivity module

The CRTM surface emissivity module is split into 8 sub-modules to accommodate new model implementations and model improvement.

IR Sea Surface Emission Model (IRSSE)

c0 – c4 are regression coefficients, obtained through regression against Wu-Smith model.

( ) ( ) ( ) ( ) ( ) ( )νν θνθνννθε ,3

,10

42 ˆ,ˆ,,,, wcwc wcwcwcw ++=

The IRSSE model is aparameterized Wu-Smith model for rough sea surface emissivity

IR emissivity lookup table for land surfaces

Surface Type

Compacted soil Grass scrub

Tilled soil Oil grass

Sand Urban concrete

Rock Pine brush

Irrigated low vegetation Broadleaf brush

Meadow grass Wet soil

Scrub Scrub soil

Broadleaf forest Broadleaf(70)/Pine(30)

Pine forest Water

Tundra Old snow

Grass soil Fresh snow

Broadleaf/Pine forest New ice

Surface types included in the IR emissivity database (Carter et al., 2002):

Microwave Ocean Emissivity Model

Model inputs: satellite zenith angle, water temperature, surface wind speed, and frequency

Model outputs:emissivity (Vertical polarization) and emissivity (horizontal polarization)

FASTEM-1 (English and Hewison, 1998):

NESDIS Microwave Land Emission Model (LandEM)

(1) Three layer medium:

)(,,2 2 TBLayer ε

desert, canopy, …

)1( 120 RI −

120RI )1)(,( 210 RI −μτ0I

1,1 εLayer

3,3 εLayer)(31 TBeI =

),( 1 μτ −I231 ),( RI μτ −

0τ

1τ

(2) Emissivity derived from a two-stream radiative transfer solution and modifiedFresnel equations for reflection and transmission at layer interfaces:

)(22121

)(212

)(2

2112 01

0101

)()1(])[1(]1)[1()1( ττ

ττττ

γββγβαγβαε −−

−−−−

−−−−−++−

−+= k

kk

eRReReRR

Weng, et al, 2001

Conditions using LandEM:over land: f < 80 GHz, use LandEM; f >= 80 GHz, e_v = e_h = 0.95over snow: f < 80 GHz, use LandEM; f >= 80 GHz, e_v = e_h = 0.90

(1) Emissivity Database:

ϑcos)( 332

12

110 aTaTaTaaDI SBj

N

jjBj

N

jji ++++= ∑∑

==

(2) Snow type discriminators are used to pick up snow type and emissivity:

Tb,j – e.g. AMSU window channelmeasurements

Microwave empirical snow and ice surface emissivity model

(3) Supported sensors: AMSU, AMSRE, SSMI, MSU, SSMIS

Radiative transfer solution under clear sky conditions

sunsunssnns

n

kkkk FpITBTBI θπθτρτετεττ ννννννννννννν cos)/)(,()1()()()( ,0,,

1,1, +−++−= ↓

=−∑

(4)

∑= =

−k

jj

ek1

)cos(/ θσ

τTransmittance at the kth level:

σk – optical depth of the kth layer

(1) (2) (3)

(1) Contribution from the atmospheric absorbing gases;(2) Contribution from surface emission attenuated by the atmosphere(3) Surface reflected downwelling radiation from the atmosphere and space cosmic

background attenuated by the atmosphere.

(4) Surface reflected solar radiation attenuated by the atmosphere

cdn

n

kkdkdkds ITBI )()())()(()( ,

11,,, θτθτθτθ ννννν

↓

=

−↓↓↓ +−=∑

MW: θd – satellite zenith angle(specular surface reflection)

IR : θd – diffuse angle(Lambersian surface reflection)

Weight function and radiance Jacobian

)/()( 1,1, kkkkk zzw −−= −− νν ττ))ln()/(ln()( 1,1, −− −−= kkkkk ppw νν ττ

kxI

∂∂

Jacobian (radiance derivative with respect to state variables):

xk - air temperature, water vapor mixing ratio, etc

or

Weighting function:

(1) The atmosphere contribution (the first term of the RT solution in the previous slide) can be express as

∑=

Δ=n

kkkk

atm TBwzI1

, )(ννν

(a) The atmospheric contribution is the weighted sum of the source functions;(b) The weighting function tells the relative importance of the contribution from

each atmospheric layer.(c) Weighting function does not depend on the layer thickness.

(2) The Jacobian is the radiance response to a unit perturbation of the state variable; it depends on the layer thickness.

TOA

Emission decreases

}Layer contribution

When the layer moves up

Attenuationdecreases

Weighting function and Jacobian profiles A

MSU

AM

HS

ch14

ch13

ch12

ch11

ch9ch10

ch6ch7ch8

ch4ch5

ch2ch1

ch3

ch4

ch5

Computed with CRTM for US standard atmosphere over ocean surface

Weighting function Jacobian with respect to temperature

Jacobian with respect to H2O mixing ratio times layer mixing ratio

CRTM fast transmittance model

• Microwave and infrared spectra• Why we need fast algorithm• Transmittance parameterization

There are other well known transmittance models: RTTOV (UK), OSS (AER, Inc) and SARTA (UMBC). The JCSDA RT team is integrating them into CRTM.

Microwave transmittance spectrum

MW O2 transmittance near 60 GHz

Be = 60 µTBe – Earth’s magnetic field strength.θB – angle between the observation direction and the Earth’s magnetic field.

Zeeman-splitting effect (9+, left-circular polarization)

IR total transmittance spectrum (1)

IR total transmittance spectrum (2)

HIRS/3 spectral response functions (SRFs)

Fast transmittance module

∑=

=N

ivch ii

II1

φν

In the atmosphere, the absorption line width αL isabout 0.05 cm-1 at 1000mb and 0.0125 cm-1 at 250 mb. So, e.g., for a sensor with 1 cm-1

passband, a large number of monochromatic radiance calculations are needed for channel radiance simulation:

ki

n

ikikkch xcc ,

1,,0, ∑

=

+=σ

∑=

≡N

ivkkch ii

1,, φττ ν

Why need fast algorithm:

Current operational systems can not handle such computation.

Solution: parameterize the optical depth σch,k, defined as

The channel’s spectral response function (SRF)

and)/ln( ,1,, kchkchkch ττσ −≡

Parameterization: Predictors, such as T and water vapor

The radiance is then computed with the regular RT equation without the need for spectral integration.

CRTM currently is implemented with the OPTRAN transmittance algorithm

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

wavenumber offset from line center, cm-1

w idth=0.0125cm-1p=250mb

w idth=0.025cm-1 p=500mb

w idth=0.05cm-1 p=1000mb

From Goody

0

0.02

0.04

0.06

0.08

0.1

1 3 5 7 9 11 13 15 17 19AMSU channel number

RM

S fit

ting

erro

rTotalDryWater Vapor

0

0.05

0.1

0.15

0.2

0.25

1 3 5 7 9 11 13 15 17 19HIRS channel number

RM

S fit

ting

erro

r (K

)

TotalDryWater vaporOzone

Radiance errors due to transmittance model uncertainty

Radiance Jacobians with respect to water vapor, compared with LBLRTM

Without including Zeeman-effect in the model.

Collocated temperature profiles for model input are retrievals form the SABER experiment.Sample size: 1097 samples

Comparison between SSMIS observations and simulations with/without Zeeman-effect

Channels 23 & 24 are not affected by Zeeman-splitting

CRTM cloud absorption/scattering, aerosol absorption/scattering and RT solution modules

Cloud absorption/Scattering module (provide cloud optical parameters for RT solution module)

• Six cloud types: water, ice, rain, snow, graupel and hail• NESDIS/ORA lookup table (Liu et al., 2005): mass extinction

coefficient, single scattering albedo, asymmetric factor and Legendrephase coefficients. Sources: − IR: spherical water cloud droplets (Simmer, 1994); non-spherical

ice cloud particles (Liou and Yang, 1995; Macke, Mishenko et al.; Baum et al., 2001).

− MW: spherical cloud, rain and ice particles (Simmer, 1994).

Aerosol absorption/Scattering module (provide aerosol optical parameters for RT solution module)

Dust

0.000.100.200.300.400.500.600.70

0 5 10 15 20 25 30 35 40

wavelength

mas

s ex

tinct

ion

1.4

2.5

8

Dust

0.00

0.20

0.40

0.60

0.80

1.00

0 5 10 15 20 25 30 35 40

wavelength

albe

do

1.42.58

• GOCART aerosol profiles: Dust, Sea Salt, Organic carbon, Black carbon, Sulfate.

• Optical parameter lookup table.

Dust

0.00

0.20

0.40

0.60

0.80

1.00

0 5 10 15 20 25 30 35 40

wavelength

asym

met

ry fa

cto

1.42.58

Size μm

RT solution for cloud/aerosol scattering environment: Advanced Doubling-Adding Method (ADA)

AtmOpticsOptical depth, single scattering

Albedo, asymmetry factor,Legendre coefficients for

phase matrix

Planck functionsPlanck_Atmosphere

Planck_Surface

SfcOpticsSurface emissivity

reflectivity

Compute the emitted radiance and reflectance at the surface

(without atmosphere)

Compute layer transmittance,reflectance matrices by doubling

method.

Combine (transmittance, reflectance,upwelling source) current level and added

layers to new level

Output radiance

Loopfrom bottom totop layers

(New algorithm) compute layer sources from above layer transmittance and

Reflectance analytically.

Liu and Weng, 20061.7 times faster then VDISORT; 61 times faster than DAMaximum differences between ADA,VDISORT and DA are less than 0.01 K.

Model simulations with cloud component on (black) and off (yellow);AMSU-A and MHS observations (red), 07/27/2006Model input: cloud liquid/ice content and particle size profiles from CloudSat

Cloud classification

Rain rate near surface

Upper two panels:Red – AMSUA+MHS retrievals Black – derived from CloudSat Radar

Time series of AMSU-A, MHS observations versus CRTM simulations using CloudSat data (non-precipitating weather)

Large differences between Observations and simulations near 3.1 are due to CloudSatdata that exclude precipitation.

Time series of AVHRR observations versus CRTM simulations using CloudSat data

• Model simulations with cloud component on (black) and off (blue)• AVHRR observations (red)• Model input: cloud liquid/ice content and particle size profiles from CloudSat

Cloud classification Cloud classification

Mean & RMS difference between AMSU-A, MHS & AVHRR observations and simulations under cloudy conditions

Mean difference (obs – simulation with cloud component on)Mean difference (obs – simulation with cloud component off)RMS difference (obs – simulation with cloud component on)Mean difference (obs – simulation with cloud component off)



Mean & RMS Diff. (obs. – simulation w. cloud off)Mean & RMS Diff. (obs. – simulation w. cloud on)

The differences between the observations and simulations are significantly reduced with the inclusion of modeling cloud absorption and scattering

AM

SU-A

23.8GHz

31.4GHz

50.3GHz 89.0GHz

89.0GHz 150.0GHz927.6 cm-1 833.2 cm-1

Sample size = 1020

Sample size = 3396

Sample size = 10692

AV

HR

R

MH

S

CRTM Tangent-linear, Adjoint and K-Matrix (Jacobian) models

Order of developing these models:

MatrixKADTLFW _⇒⇒⇒

)(XFY =

TmyyyY },...,,{ 21=

TnxxxX },...,,{ 21=

• Forward model:

Radiance vector (m channels)

State vector (n state variables)

)])([(...)( 012 XZFFFXF K ==

FW model may be considered as a composition of a set of K functions:

YZFZZFZXZFZ kkklll ===== −− )(...,),(...,),( 11011

or expressed with the help of the intermediate variables Zl as

In CRTM, many of the functions are coded explicitly with subroutines or functions:

)( 1−= lll ZFZ

Zl-1 – input variable vectorZl – output variable vector

(1)

(2)

• Tangent-linear (TL) model:

XXHY δδ )(=

YδXδ

perturbation of Yperturbation of X

},1;,1,{, njmixyH

j

iji ==

∂∂

=

H(X), a matrix with elements:Jacobians (derivatives of the radiance with respect to a state variable)

0011211 )()()()( ZZHZHZHZHY llKKKK δδ ⋅⋅⋅⋅⋅⋅= −−−−

Applying the chain rule to (1):

}{}{)( 1,1

jl

il

jilll

ZFHZH −

−

∂∂

==

11110011 )(,)(,......,)( −−−− ==== kkkkllll ZZHZZZHZZXZHZ δδδδδδ

In CRTM, is developed by differentiating the FW counterpart .

11)( −−= llll ZZHZ δδ11, −− ll ZZ δ

lZδ

or expressed as

Inputs

where

)( 1−= lll ZFZ

Naming convention: (1) If Z is a FW variable name, then δZ is named is Z_TL; (2) if Sub is the FW subroutine (or function) name, then the corresponding Tangent-linear subroutine (or function) is named as Sub_TL.

Output

• Adjoint (AD) model:

Let the function J(.) transforms the radiance vector Y (=F(X)) into a scalar:

J = J(Y)

The gradient of J with respect to X:JYJ YXX ∇∇=∇

T

nX x

JxJJ ],...,[

1 ∂∂

∂∂

=∇ T

mY y

JyJJ ],...,[

1 ∂∂

∂∂

=∇

},1;,1,{ minjxyY

j

iX ==

∂∂

=∇

(Note, CRTM does not include this function)

XZZFZ lll == − 01 ......,),(Since )])(...[()( 11 llkkk ZFFFFXFY −−==and

))))((...((( 21 llkkk ZFFFFJJ −−= So J is also a function Zl

Define Adjoint variables:

JYJXJZ YXZl

l ∇≡∇≡∇≡ *** ,, δδδ

where both vectors

transpose of the Jacobian matrix

we have

--- AD model

JYJ YXX ∇∇=∇

YHHHYXHX

TKTT

T

*21

**

)()()()(

δ

δδ

⋅⋅⋅=

=Into the form:So we can write

1*1*2*21*1*12**1* )(,)(,,)(,)( ZHXZHZZHZYHZ TTKTKKTKK δδδδδδδδ ==⋅⋅⋅== −−−−

or

llTll ZZHZ *11* )()( δδ −− =In CRTM, is developed by reversing the order of the operations in the TL counterpart , following a set of rules (Giering and Kaminski, 1998)

1−lZ1* −lZδ

lZ*δ InputOutput

11)( −−= llll ZZHZ δδ

Naming convention: if Z is the FW variable, the corresponding AD variable is named as Z_AD; if Sub is the FW routine, then Sub_AD is named as the AD routine.

Adjoint (AD) model (Cont.):

• The outputs of the TL and AD models:

TL model provides:

mi

xxyx

xyx

xyy n

n

iiii

,1

...22

11

=∂∂

++∂∂

+∂∂

= δδδδ

XXHY δδ )(=

or

AD model provides: YXHX T ** )( δδ =

or

nj

yxyy

xyy

xyx m

j

m

jjj

,1

... *2

*21

*1*

=

∂∂

++∂∂

+∂∂

= δδδδ

(1) are the AD model input variables. If they hold the values , then the output hold the values --- the

gradient of the J function.

(2) The TL and AD models do not provide Jacobians unless you set one of the inputs δxj = 1 for the TL model and δ*yi = 1 for the AD model and set the reset of the delta inputs to zero and loop over the range of i or j --- a slow process.

},1,{ * miyi =δ}),1,/{( miyJJ iY =∂∂=∇ jx*δ JX∇

A summation over the state variable dimension

A summation over the channel dimension

• K-matrix model (compute the Jacobian matrix H):

],...,,[_ *2

*21

*1 mm yhyhyhKX δδδ=

K-matrix model is a slightly modified version of the AD model; The modification is to separate the terms in the summation expression (see previous side). The K-matrix model may be expressed as

T

n

iiii x

yxy

xyh ],...,,[

21 ∂∂

∂∂

∂∂

=where

};,1,{},1;,1;{_ *,

* njmiyxynjmixKX i

j

iji ==

∂∂

==== δδ

iji yxy *)/( δ∂∂

δ*y1, …, δ*ym are part of the K-matrix model input variables

Naming convention: in CRTM K-Matrix model, δ*xi,j is named as x_K and δ*yi as y_K.

To obtain Jacobians, set all the inputs δ*y1, …, δ*ym to one.

CRTM user interface (1)

• CRTM software characteristic:− A set of Fortran subroutines and functions; users call CRTM from their

application programs.− Structure variables (derived types) are used as input and output variables in the

routine interfaces.Benefits: (1) clean, (2) adding variables does not change the interfacesDisadvantages: (1) variables are hidden under the structure variable name (e.g. X.x1 and X.x2 are hidden in the interface where only X appears; (2) it is easy to forget initialize those variables that are not interested to the users.

− There is a set of coefficient data that are loaded during CRTM initialization stage. These data are included in several files, some of which are sensor/channel independent and some are sensor/channel dependent.

CRTM User Interface (2)• CRTM Calling procedure (an example):

{

CRTM Initialization (load coefficient data)In this process, the set of sensors supported in the following calls are determined.

Memory allocation (using CRTM routines) for structure pointer array members

Sensor selection (among the sensors specified during CRTM initialization)

CRTM FW model

Set CRTM input variables

CRTM TL model CRTM AD model CRTM KM model

Memory deallocation (using CRTM routines) for allocated structure pointer array members

CRTM destruction (deallocate memory for internal variables)

oror or

or

Ending process {

May

be

repe

ated

CRTM User Interface (3)

• CRTM initialization:Error_status = CRTM_Init( ChannelInfo , & ! Output

SensorID , & ! inputCloudCoeff_File , & ! inputAerosolCoeff_File , & ! inputEmisCoeff_File ) ! Input

SensorID : string array containing a list of the sensor IDs (e.g. hirs3_n17, amsua_n18, etc); array size = n_sensors specified by the user. The sensor IDs are used to construct the files for the SpcCoeff and TauCoeff file names:

e.g. hirs3_n17 will be used for hirs3_n17.SpcCoeff.bin and hirs3_n17.TauCoeff.bin

CloudCoeff_File, ArosolCoeff, EmisCoeff: file names for coefficient data file used for cloud, aerosol, surface emission and scattering calculations; the data are currently not sensor specific. ChannelInfo : structure array (type ChannelInfor_type) containing sensor/channel information when returned from this function, array size = n_sensors.

• CRTM destruction:Error_status = CRTM_Destroy( ChannelInfo )

(1) The memory for ChannelInfo is released, (2) all dynamically allocated memory for internal variables is released.

CRTM User Interface (4)• Calling CRTM FW model (example):

Error_Status = CRTM_Forward( Atmosphere , & ! InputSurface , & ! Input GeometryInfo , & ! Input ChannelInfo(2:2) , & ! InputRTSolution ) ! Output

Atmosphere: structure array (type Atmosphere_type) containing data describing atmospheric state; array size = n_profiles (specified by user).e.g. Atmospere(1)%temperature is an array of size n_layers (specified by user) containing the temperature profile for the first atmospheric profile. Surface: structure array (type Surface_type) of size n_profiles containing data describing surface state. e.g. Surface(1)%water_temperature is a scalar variable for the water surface temperature.GeometryInfo: structure array (type GeometryInfo_type) of size n_profilescontaining satellite/sensor geometry information. e.g. the scalar GeometryInfo%Sensor_Zenith_Angle describes the sensor’s zenith angle.ChannelInfo: explained in the previous slide; ChannelInfo(2:2) is a one-element array containing sensor/channel information for the second sensor, which the user specified with the SensorID array during CRTM initialization. RTSolution: structure array (type RTSolution_type) of size ChannelInfo(2:2) %n_Channels x n_profiles. e.g. the scalar variable RTSolution(1,1)%brightness_temeprature is the BT for the first channel and first profile.

CRTM User Interface (5)• Calling CRTM TL model (example):

Error_Status = CRTM_Tangent_Linear( &Atmosphere, Surface & ! InputAtmosphere_TL Surface_TL , & ! Input GeometryInfo , & ! Input ChannelInfo(2:2) , & ! InputRTSolution, RTSolution_TL) ! Output

Atmosphere_TL: structure array of the same type and dimension as Atmosphere containing TL variables corresponding to those in Atmosphere.Surface_TL: structure array of the same type and dimension as Surface containing TL variables corresponding to those in Surface.RTSolution_TL: structure array of the same type and dimension as RTSolutioncontaining the resulting TL variables corresponding to those in RTSolution.

e.g. Atmosphere_TL(1)%temperature(10) is the temperature perturbation at layer 10 of the first profile and RTSolution_TL(1,1)%brightness_temperature is the response to the perturbations of those variables in Atmosphere_TL and Surface_TL for the first channel and first profile.

Note, when calling this routine, make sure all the perturbations are correctly set. E.g. Surface%wind_speed has a default value of 5 m/s. Since Surface_TL has the same type Surface_type as Surface, Surface_TL%wind_speed (perturbation) is automatically set to 5 m/s. So it must be set to zero or the intended value.


• Calling CRTM AD model (example):

RTSolution_AD: structure array of the same type and dimension as RTSolutioncontaining the AD variables corresponding to those in RTSolution.Atmosphere_AD: structure array of the same type and dimension as Atmosphere containing AD variables corresponding to those in Atmosphere.Surface_AD: structure array of the same type and dimension as Surface containing AD variables corresponding to those in Surface.

Error_status = CRTM_Adjoint( Atmosphere, Surface , & ! InputRTSolution_AD , & ! Input GeometryInfo, ChannelInfo(2:2) , & ! InputAtmosphere_AD, Surface_AD , & ! OutputRTSolution) ! Output


• Calling CRTM K-Matirx model (example):

ij

i yxy *δ∂∂

Note:(1) compared with Atmosphere_AD and Surface_AD in the AD model, Atmosphere_K and Surface_K have an additional dimension n_Channels (as mentioned earlier, this dimension separates term from the other terms.

(2) To request a brightness temperature Jacobians , in this example, set RTSolution_K(i,1)%brightness_temperature = 1.0 and RTSolution_K%radiance = 0.0, i=1,n_Channels.

ji xBT

RTSolution_K: structure array of the same type and dimension as RTSolutioncontaining the K variables corresponding to those in RTSolution.Atmosphere_K: structure array of the type Atmosphere_type with dimension n_Channels x n_profiles, containing K variables corresponding to those in Atmosphere. Surface_K: structure array of the type Surface_type with dimension n_Channelsx n_profiles, containing K variables corresponding to those in Surface.

Error_Status = CRTM_K_Matrix( Atmosphere, Surface , & ! InputRTSolution_K , & ! InputGeometryInfo, ChannelInfo(2:2) , & ! InputAtmosphere_K, Surface_K , & ! OutputRTSolution ) ! Output

∂∂ /

Explain why need setting one of Radiance_K & BT_K to one and the other to zero

In the FW routine Compute_FW(X, Rad, BT):

CALL Compute_Radiance(X, Rad)CALL Compute_BrightnessTmperature(…, Rad, BT)

In TL routine Compute_TL(X, X_TL, Rad_TL, BT_TL):

CALL Compute_Radiance_TL(…, X_TL, Rad_TL)CALL Compute_BrightnessTemperature_TL(…, Rad_TL, BT_TL)

In AD routine Compute_AD(X, Rad_AD, BT_AD, X_AD):

CALL Compute_BrightnessTemperature_AD(…, BT_AD, Rad_AD)CALL Compute_Radiance_AD(Rad_AD, X_AD)

In Compute_BrightnessTemperature_AD(…, BT_AD, Rad_AD):….Rad_AD = Rad_AD + a*BT_ADBT_AD = 0.

In Compute_Radiance_AD(Rad_AD, X_AD):….

X_AD = X_AD + b*Rad_ADRad_AD = 0

Red color – input variablesBlack color – output variables

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